The 42-year-old has 18 months left on his existing deal at Stamford Bridge having succeeded Maurizio Sarri in July 2019.
Lampard arrived with the club serving a FIFA transfer ban relating to rule breaches on signing players under the age of 18, a restriction compounded by the loss of talisman Eden Hazard to Real Madrid last summer.
However, Chelsea qualified for the Champions League in his first season before making up for lost time in the market, signing six players including Kai Havertz, Timo Werner and Hakim Ziyech who have helped them climb to third in the Premier League, just two points behind leaders Tottenham.
"In terms of my contract, it seems to have flown by, the time that I've been here. And you are right, I've got 18 months left," Lampard said at a news conference on Friday when asked whether he would hope to see his contract extended.
"I feel, and I felt it when I actually came to the club, I knew there were a lot of circumstances at the beginning that were going to make last year transitional, maybe slightly difficult. I felt like I took the job in a different position to most recent Chelsea managers. I think people sympathised with that and I thought it was a success.
"Now I would love to be part of the long-term plan here. The signings we made in the summer, other than probably [36-year-old] Thiago [Silva] particularly, were signings for now and the future -- players that are going to progress and that I think are going to mature. And of course I'd love to be part of that.
"Of course, that's the club's decision and the owner's decision, first and foremost. I have to get on with the short term which is the only thing which starts with Leeds tomorrow.
"I don't think anyone would expect me to say anything else. I'm a lucky man to be managing the club that I love and is my life. Of course, I want to make a success of it and be here as long as I can.
"I can only ever look at what's in front of me and at the minute, since I came in here actually, the relationship I had with [technical advisor and former team-mate] Petr Cech has been a huge strength for me because I get on so well with him and I think hopefully we work well together. The communication I have with [director] Marina [Granovskaia] is very regular. I try and do all things I can do for the best of the club, on and off the pitch, and I can't get much further down the line than that.
"I've said before I'd like to do this job as long as possible but I'm also very aware that is results based. At the minute, I think we are working towards something, people are getting very excited and mentioning us being in the title race this year. I always saw it as a longer plan than that and it might take until next year for us to really challenge because of the signings and the bedding in process."
Another of Lampard's former team-mates, Branislav Ivanovic, has claimed the ex-midfielder, who has 106 international caps, could one day manage the England team.
Gareth Southgate has a contract until after the 2022 World Cup.
"I appreciate Brana's words. He's a good friend so I appreciate the positive wording there," Lampard said.
"It is certainly not anything that is on my short-term radar. I'm very patriotic, I loved playing for my country but at the moment I am focused on trying to do the best thing here in a long-term way, it is all I can l think about. I appreciate it. If it was ever an opportunity later on down the line, it is something I certainly would look at. But you should never look too far down the line I think in this job."